Editing colors in Blender for vibrance and saturation
Besides the postproduction options outlined in other answers, you can be intentional on how you use the elements instead of resorting to &quot;fixing in post&quot;. You do have absolute control on the quality of the scene by careful crafting of the materials used and the lighting of the scene, without having to resort to additional effects.
If you want more saturated colors... use more saturated colors, or darker colors, in the shaders those are the ones that determine the color of an object in the scene, you have total control on how objects reflect light or how shiny they are. Also make sure that the intensity, and quality, of your lights is not making the objects too bright, and that is helping you get what you want.
Also play a bit with the different looks on the color management section. A higher contrast might be useful.

Read both answers on the following link very carefully:
Desaturated red when rendered
And read the whole page (comments and answers) here:
How can I get more saturated colors when I render?
To understand the relationship between brightness and saturation on the filmic color transform read this as well:
Render with a wider dynamic range in cycles to produce photorealistic looking images